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Chapter 1: Q. 43 (page 107)
For each limit statement in Exercises , use algebra to find or in terms of or , according to the appropriate formal limit definition.
, findin terms of.
For,.
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Write delta-epsilon proofs for each of the limit statements in Exercises .
.
Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.
Sketch the graph of a function f described in Exercises 27鈥�32, if possible. If it is not possible, explain why not.
f is left continuous at x = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = 鈭�2.
For each limit statement , use algebra to find 未 > 0 in terms of > 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < .
For each limit statement , use algebra to find 未 > 0 in terms of > 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < .
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